analyzing the effects of particle density, size and size … · 2017-09-26 · analyzing the...

Analyzing the Effects of Particle Density, Size and Size Distribution

for Minimum Fluidization Velocity with Eulerian-Lagrangian CFD

Simulation

Janitha C. Bandara1 Marianne S. Eikeland1 Britt M. E. Moldestad1 1Faculty of Technology, Natural Sciences and Maritime Sciences, University College of Southeast Norway

{Janitha.bandara, Marianne.Eikeland, britt.moldestad}@usn.no

Abstract

Fluidized bed reactor systems are widely used due to

excellent heat and mass transfer characteristics followed

by uniform temperature distribution throughout the

reactor volume. The importance of fluidized beds is

further demonstrated in high exothermic reactions such

as combustion and gasification where fluidization

avoids the hot spot and cold spot generation. A bed

material, such as sand or catalyst, is normally involved

in fluidized bed combustion and gasification of biomass.

Therefore, it is vital to analyze the hydrodynamics of

bed material, especially the minimum fluidization

velocity, as it governs the fluid flowrate into the reactor

system. There are limitations in experimental

investigations of fluidized beds such as observing the

bed interior hydrodynamics, where CFD simulations has

become a meaningful way with the high computer

power. However, due to the large differences in scales

from the particle to the reactor geometry, complex

interface momentum transfer and particle collisions,

CFD modeling and simulation of particle systems are

rather difficult. Multiphase particle-in-cell method is an

efficient version of Eulerian-Lagrangian modeling and

Barracuda VR commercial package was used in this

work to analyze the minimum fluidization velocity of

particles depending on size, density and size

distribution.

Wen-YU-Ergun drag model was used to model the

interface momentum transfer where default equations

and constants were used for other models. The effect of

the particle size was analyzed using monodispersed

Silica particles with diameters from 400 to 800 microns.

Minimum fluidization velocity was increased with

particle diameter, where it was 0.225 m/s for the 600

microns particles. The density effect was analyzed for

600 microns particles with seven different density

values and the minimum fluidization velocity again

showed proportionality to the density. The effect of the

particle size distribution was analyzed using Silica.

Particles with different diameters were mixed together

according to pre-determined proportions as the final

mixture gives a mean diameter of 600 microns. The 600

microns monodispersed particle bed showed the highest

minimum fluidization velocity. However, some particle mixtures were composed with larger particles up to 1000

micron, but with a fraction of smaller particles down to

200 microns at the same time. This shows the effect of

strong drag from early fluidizing smaller particles. The

only variability for pressure drop during packed bed is

the particle size and it was clearly observed in all three

cases.

Keywords: Fluidization, Bioenergy, Particle

properties, Minimum fluidization velocity

1 Introduction

Fluidization occurs whenever a collection of particles is

subjected to an upward fluid flow at a sufficient flowrate

where the gravity and inter-particle forces are in

counterbalance with the fluid drag force (Horio 2013).

The fluidized bed technology was first introduced in the

petroleum industry for catalytic cracking processes,

which later penetrated into energy, environmental and

processing industry (Horio 2013, Winter and Schratzer

2013, Vollmari, Jasevičius et al. 2016). The technology

enhances the gas-solid contact and mixing, which leads

to increased heat and mass transfer characteristics.

Further, it guarantees the homogeneous temperature and

concentrations throughout the reactor, which increases

the possibility and reliability of scaled up operation.

Good control over solid particles, large thermal inertia

of solids (Esmaili and Mahinpey 2011), increased

efficiency, reduced emissions and wide range of

operating conditions are additional advantages of the

fluidized bed systems (Winter and Schratzer 2013). The

importance of the fluidized bed technology is

highlighted specially in exothermic reactions such as

biomass combustion as it avoids hot spot and cold spot

generation due to intense mixing and particle collision.

Hot spots lead to ash melting followed by agglomeration

and clinkering (Behjat, Shahhosseini et al. 2008, Horio

2013) whereas cold spots reduces tar cracking and thus,

reduced gas quality.

Bio-energy is the fourth largest energy source, which

accounts for 10% to 14% of the world energy profile

(REN21 2016). The lignocellulosic fraction of the

biomass is the major contributor of bioenergy. In

contrast to the simple, inefficient and small-scaled

combustion practices, there is a tendency to use

advanced technologies such as fluidized bed

gasification followed by either heat & power generation or liquid fuel synthesis. However, due to low density,

large particle size and extreme shapes of the particles,

DOI: 10.3384/ecp1713860 Proceedings of the 58th SIMS September 25th - 27th, Reykjavik, Iceland

60

biomass is difficult to fluidize alone (Cui and Grace

2007). Therefore, biomass fluidized bed combustors and

gasifiers are operated with the assistance of fluidizing

materials such as sand, alumina, catalysts etc., which is

known as bed material (Fotovat, Ansart et al. 2015).

Hence, it is meaningful to study the fluidization

behavior of bed materials as it principally governs the

bed hydrodynamics. Bubbling fluidization stands

slightly above the minimum fluidization. Hence, it is

important to manipulate the minimum fluidization

velocity in bubbling fluidized bed gasification systems,

because it governs the mass flowrate of gasifying agent

into the reactor system.

The fluidization properties are governed by both

particle properties such as particle size, particle density,

particle shape etc. and fluid properties (Fotovat, Ansart

et al. 2015). However, there can be additional effects

from the bed diameter, geometry, aspect ratio and

distributor design as well. The transition superficial gas

velocity from fixed bed to fluidized bed is referred to as

the minimum fluidization velocity, which is one of the

most important parameters in the design of fluidized

beds (Coltters and Rivas 2004). Depending on Geldart’s

powder classification and superficial gas velocity,

particles tend to fluidize in homogeneous, bubbling,

slugging or sprouting beds (Geldart 1973).

Computational Fluid Dynamics (CFD) simulations

are beginning to appear in a meaningful way with the

tremendous growth in computer power along with

sophisticated mathematical models and efficient

algorithms (Cooper and Coronella 2005, Kia and

Aminian 2017). The faster and more accurate CFD

simulations of fluidization systems, makes it easier to

get detailed predictions compared to the expensive and

time consuming experiments. On the other hand, CFD is

a smart tool in optimizing the geometry, which is

difficult or even impossible to achieve with

experiments. Further, it provides an insight into the bed

interior, which again is difficult to achieve with

experiments unless more advanced technologies are

used. Extreme operational conditions can also be

analyzed in advanced to guarantee the safe operation of

experimental setups.

However, modeling of gas-solid flow behavior is

challenging due to the complexities arising from the

coupling of turbulent gas flow and particle motions

together with inter-particle collisions. The differences in

scale from particles to geometry is another difficult

parameter in the CDF simulations. Lagrangian-Eulerian

and Eulerian-Eulerian are the basic modeling

approaches in gas-solid multiphase systems.

Lagrangian-Eulerian modeling solves the Newtonian

equation of motion for each individual particle in the

system while the gas phase is modeled as a continuum

with Navier-Stokes equations. In contrast, the Eulerian-

Eulerian modeling considers both phases as continuous

and interpenetrating, which are modeled with the

Navier-Stokes equations (Xie, Zhong et al. 2013). Even

though Eulerian-Eulerian modeling consumes less

computer power, it is complex in modeling stage, as it

needs more closure functions. In contrast, the

Lagrangian-Eulerian simulations need high computer

power, and it is unrealistic to use for industrial scale

reactors. Multiphase particle-in-cell (MP-PIC) was

developed as an extension to the Lagrangian-Eulerian

simulations, where particle are modeled in both discrete

and continuous phase (Snider 2001, Xie, Zhong et al.

2013). Instead of individual particles, it considers

groups of particles sharing common characteristics.

These groups are referred to as parcels or computational

particles. Particle properties that are best calculated on

the grid are calculated using continuous modeling in the

advanced time step and interpolated back to individual

particles. The successive development of the MP-PIC

method is illustrated in the works of Snider, O’Rourke

and Andrew s (Andrews and O'Rourke 1996, Snider,

O’Rourke et al. 1998, Snider 2001, Snider 2007,

O'Rourke and Snider 2012). This particular method is

embedded in Barracuda VR commercial software

package, which is becoming popular in CFD modeling

of gas-solid systems and has brought forward the

concept of computational particle fluid dynamics

(CPFD). Hence, the objective of this work is to analyze

the effect of particle properties of density, size and size

distribution on the minimum fluidization velocity with

CPFD simulation.

2 Methods and Computational Setup

Barracuda VR 17.1.0 was used for the simulations

where a simple cylindrical geometry of 1000 mm in

height and 84mm in diameter was considered. A

uniform grid was applied with 8000 cells in total, which

is illustrated in Figure 1. Grid refinements at the wall

was not performed as it was assumed that there was no

boundary layer formation with the dense phase particle

system. Default grid generator settings were used, which

removes the cells having less fraction of volume than

0.04 and greater aspect ratio than 15:1.

Isothermal temperature of 300 K was used where sand

(SiO2) was used as the basic bed material. However,

other materials as aluminum oxide (Al2O3), nickel oxide

(NiO), calcium (Ca), ferric oxide (Fe2O3), titanium

oxide (TiO2) and zirconium (ZrO2) were used to analyze

the effect of density on the minimum fluidization

velocity. Air at atmospheric pressure was used as

fluidizing gas in all the cases. Particles were filled up to

350mm of height and the random packing option was

used.

The close pack volume fraction, maximum momentum

redirection from collisions, normal to wall momentum

retention and tangent to wall momentum retention were

set to 0.6, 40%, 0.3 and 0.99 respectively. Default values

for the parameters in the particle stress model were kept

unchanged. Blended acceleration model was activated


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for the mixtures of different particle sizes. The column

was operated at atmospheric pressure where the air

outlet at the top plane was defined as a pressure

boundary. Inlet boundary was defined as a flow/velocity

boundary with varying air velocities over time. Each

velocity was maintained for 4 seconds. Further, uniform

air distribution at the inlet and no particle exit from the

pressure boundary were assumed. The bed pressure was

monitored in the center of the bed at five different

heights. The boundary conditions and the pressure

monitoring points are depicted in Figure 1.

Figure 1. (a) Grid, (b) Boundary conditions, (c) Pressure

data points

3 Results and Discussion

The bed materials used in fluidized bed gasification and

combustion are usually polydispersed with a wide size

distribution. However, monodispersed particle beds

were used in this work to demonstrate the effect of

particle size for minimum fluidization velocity.

Attempts were made to analyze the effect of the particle

size mixtures later in this work.

Figure 2. Gas velocity vs pressure drop diagram (Kunii

and Levenspiel 1991)

The pressure drop (∆p) versus superficial gas velocity

𝑈0 diagram is useful in determining the transition from

fixed bed to fluidized bed. During the fixed bed

operation, the bed pressure drop is proportional to the

gas velocity. Once the bed reaches the minimum

fluidization velocity, the bed pressure drop decreases a

little, and stabilizes at the static bed pressure. The bed

continues to stay around that pressure until the particle

entrainment starts (Kunii and Levenspiel 1991). This

behavior and figuring out of the minimum fluidization

velocity 𝑈𝑚𝑓, is illustrated in Figure 2.

Fluid drag force resulted from the upward fluid flow

is one of the most important particle forces in any

fluidized bed system. Due to this, many researchers have

worked towards the optimization of drag models for

particular cases. The author has experimentally

validated the good performance of the Wen-Yu-Ergun

drag model in a previous work (Bandara, Thapa et al.

2016). Gidaspow proposed a drag model where the

interface momentum transfer coefficient, 𝐾𝑠𝑔, is

selected from either Wen-YU or Ergun correlation

depending upon the gas volume fraction (Sobieski

2009). When the gas volume fraction is greater than 0.8,

Wen-Yu correlation is applied which is given by:

𝐾 𝑠𝑔

𝑊𝑒𝑛𝑌𝑢

= 3

4

𝐶𝑑𝜌𝑔𝜀𝑔(1−𝜀𝑔)(𝑢𝑠−𝑢𝑔)

𝑑𝑝𝜀𝑔

−2.65 (1)

Where 𝐶𝑑 is:

𝐶𝑑 = {

24

𝜀𝑔𝑅𝑒𝑠[1 + 0.15(𝜀𝑔𝑅𝑒𝑠)

0.687] , 𝑅𝑒𝑠 ≤ 1000

0.44, 𝑅𝑒𝑠 > 1000 (2)

When the gas volume fraction is less than 0.8, Ergun

correlation is used which is given by:

𝐾 𝑠𝑔

𝐸𝑟𝑔𝑢𝑛= 150

𝜇𝑔(1−𝜀𝑔)2

𝜑2𝑑𝑝2𝜀𝑔

+ 1.75𝜌𝑔(𝑢𝑔−𝑢𝑠)(1−𝜀𝑔)

𝜑𝑑𝑝 (3)

Where, subscripts g, p and s refer to gas phase,

particle and solid phase respectively. U is the velocity,

ρ is the density ε is the volume fractions, φ is the

sphericity, μ is the viscosity, Re is the Reynold’s

number and d is the particle diameter.

3.1 Effect of the Particle Size

Geldart has worked towards classifying the particles

according to both size and density in the early 1970s

(Geldart 1973). Same author has discussed the effect of

the particle size distribution in fluidized beds in a

separate publication. This work analyses these effects

from computational fluid dynamic aspects. To

demonstrate the effect of the particle size, sand particles

from 400 to 800 microns were used. The particle density was 2200 kg/m3 and it was further assumed that the

particles were spherical. As shown in Figure 3, the


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Figure 3. Minimum fluidization velocity plots for different size particles. Right upper corner sub-plot illustrates the pressure

drop during fixed bed at two different gas velocities

Figure 4: Effect of the particle density for minimum fluidization velocity

minimum fluidization velocity increases linearly with

the particle diameter as expected. Bed pressure drop

shows a linear relationship with the superficial gas

velocity during the packed bed region. Further, it is clear

from the figure that the bed pressure drop at the

minimum fluidization is almost the same for all the

particle sizes. It is also agreeable because, the bed

weight is counter balanced by the pressure drop at the

fluidization and the bed mass was approximately constant for all the sizes. The fluctuations of the pressure

drop in the fluidizing region is also realistic which can

be observed in many experimental results as well.

3.2 Effect of the Particle Density

A 600-micron sand bed was considered as the reference

and the effect of different densities were analyzed for

600-micron particles. According to the simulation

results depicted in Figure 4, the minimum fluidization

velocity is proportional to the particle density. As the

particle diameter is similar, all the plots follow the same

line during the packed bed operation.


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Figure 5. Effect of the particle size distribution on the minimum fluidization velocity

3.3 Effect of the Particle Size Distribution

The final and major task of this work is to see the

functioning of CFD technique in predicting the

minimum fluidization velocity behavior of particle

mixtures of different sizes. Specially, empirical models

for the drag force have been developed considering

mono size particles. However, the particle drag force in

a mixture of different size particles differs compared to

that in a mono-size particle bed.

The effect of the particle size distribution was compared

with the 600-micron monodispersed silica particles.

Different particle mixtures of silica all with a mean

particle diameter as 600-micron were simulated. The

description of the particle mixtures are given in Figure

5. Particle mixtures were defined by introducing one

particle species for each size and filling them randomly

with pre-defined volume fractions, which collectively

accounts for 0.6 solid/particle volume fraction.

According to the same Figure 5, 600-micron

monodispersed particles has the highest minimum

fluidization velocity, which is approximately 0.21 m/s.

The minimum fluidization velocity of mixture C is close

to the value of the 600-micron monodispersed sample.

This might be due to the narrow size distribution of

mixture C around 600 micron. The minimum

fluidization velocity of mixtures D and E is closer to

each other, but the values are less than A and C. The

particle sizes of D and E mixtures are distributed

between 400 and 800 micron in a similar way to a

certain extent. The size distribution of pre-mentioned mixtures are in a broad range with oversized and

undersized particles than 600 micron. The mixture B,

which is having equal fractions of 400 and 800 micron

particles, shows a lower minimum fluidization velocity

compared to A, C, D and E. This particular mixture

contains half of the fraction with 400 microns, which is

comparatively less compared to 600. Finally, the

mixture F with the highest size distribution (between

200 to 1000 microns) shows the lowest minimum

fluidization velocity among the six different mixtures

considered.

It is important to note the possibility of reducing the

minimum fluidization velocity by adding a certain

fraction of smaller sized particles. As an example, even

though the mixture F contains considerable amounts of

particles larger than 600 micron, the minimum

fluidization velocity still substantially drops below the

value of monodispersed 600 microns sample. In this

situation, the larger particles are affected both by the

fluid drag force and by the momentum from smaller

particles (particle drag). According to the simulations

carried out for different diameters, smaller particles are

prone to fluidized at lower gas velocities. Therefore, the

drag force from the fine particles make the larger

particles fluidize at lower gas velocities when those are

in a mixture. However, the simulation time was

increased considerably for particle mixtures than

monodispersed particle beds.

4 Conclusion

The effects of particle size, density and size distribution

on the minimum fluidization velocity were analyzed

using the MP-PIC CFD simulation technique. Barracuda

VR commercial software package was used in all the

simulations. A previously validated model, which uses


64

the Wen-YU-Ergun model for the fluid drag, was used.

However, the model had not been validated for particles

with size distribution for several sizes. It is good to

conduct experimental analysis further to guarantee the

reproducibility of simulation data.

Minimum fluidization velocity was observed to be

linearly proportional to the particle size. On the other

hand, the minimum fluidization velocity increases

approximately by a factor of two when the particle

density is doubled. It is the pressure drop, which is more

concerned during packed bed operation. Simulation

results for different size and densities prove that it is the

particle size, which governs the pressure drop.

However, it is not easy to observe a clear relationship

between minimum fluidization velocity and particle

sizes when it comes to particle mixtures. The smaller

particles in a mixture greatly affects and reduces the

minimum fluidization velocity. Thus, this phenomenon

is useful in operating a bubbling fluidized bed reactor at

different gas velocities, simply by adding either larger

or smaller particles depending on the requirement.

Finally, the Barracuda CPFD simulations can provide

precise and quick insight into the bed hydrodynamics.

Acknowledgement The authors would like to forward their gratitude to

University College of Southeast Norway for providing

of the Barracuda VR software package and computer

facilities.

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